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## Introduction

Portfolio Analysis (PA) originated in the financial markets as a way of utilising portfolios of assets to maximise the return on investments, subject to a given level of risk. The principle is that spreading investments over a range of asset types spreads risks at the same time. Since individual assets are likely to have different and unpredictable rates of return over time, an investor may be better advised to maximise the expected rate of return and minimise the variance and co-variance of their asset portfolio as a whole, rather than managing assets individually. As long as the co-variance of assets is low then the overall portfolio risk is minimised, for a given rate of overall return. Aggregate returns for an individual investor are therefore likely to be higher when low returns on an individual stock are at least partly offset by higher returns from other stocks during the same period.

PA helps in the design of such portfolios. It highlights the trade-off between the returns on an investment and the riskiness of that investment. It measures risk by estimating the variance (standard deviation) of the portfolio return, thus a portfolio with a relatively high (low) variance is judged to have a higher (lower) risk. The information on returns and risks is used to identify a portfolio that most closely matches preferences.

## Ideal problem types

Project based analysis for future combinations for future scenarios.

Designing portfolio mixes as part of iterative pathways.

## Where has this tool been applied?

Crowe and Parker (2008) provide an empirical analysis of selecting genetic material to be used for the restoration/regeneration of a forest under uncertain climate change in Canada. The study combines RCM data with a climate impact model to estimate how different seed sources perform at specific sites under alternative climate futures. The study finds that current locations of seed populations are poor predictors of optimal future locations, confirming the need for a broad portfolio of seed sources to maintain the genetic range.

Hunt (2009) applied PA to local flood management in the UK. Three alternative adaptation measures were considered for the portfolio: hard defences, i.e. dykes; flood warning systems; and property-level resistance. The portfolio returns were measured by Net Present Value (NPV) and a clear, positive, relationship was found between return and variance, highlighting a trade-off between higher NPV of hard defences and higher uncertainty of return, with a number of portfolios found to be sub-optimal.

## Strengths and Weaknesses

The main strength of the approach is that it provides a structured way of accounting for uncertainty using combinations (portfolios) of options, which individual adaptation options do not allow. It can measure “returns” using various metrics, including physical effectiveness or economic efficiency. The use of the efficiency frontier is an effective way of presenting trade-offs.

The disadvantages include that it is resource intensive, requires a high degree of expert knowledge, and relies on the availability of quantitative data. For PA to be usefully undertaken, sufficient data is needed on parameters including the average effectiveness (or expected return), the variance, and the co-variance of return for each option over the range of climate scenarios. A minimum level of effectiveness also needs to be defined. It requires probabilistic climate information to be imposed, or an accepted assumption, such as the equal weighting of alternative scenarios.

## Process of applying this tool/method.

The steps involved are:

- Options are defined, and feasible portfolios of options are constructed.
- Investment returns (benefits) are defined and measured. This can include physical or economic metrics, e.g. quantity of water conserved or NPV.
- The risk is characterised in terms of the variance or standard deviation around the mean, using probabilities of alternative outcomes to estimate the Expected NPV (ENPV) (i.e. the sum of the products of outcomes and their associated probabilities). The variance of the NPV expresses the risk that the actual return will differ from expected return.
- The risk-return data for each portfolio is estimated by multiplying the ENPV of each asset in the portfolio by the proportion of each asset. This allows identification of efficient portfolios, i.e. with highest expected return for a given risk or – equivalently - lowest degree of risk for a given mean rate of return (Aerts et al. 2008). The results are plotted in terms of expected return and variance that identifies an efficiency frontier. Portfolios below the efficiency frontier (low returns for high risk) are omitted.
- The decision-maker then chooses a portfolio from the efficiency frontier that best represents their risk-return preferences, noting risk-averse and risk-neutral risk decision-maker would choose different portfolios.

## Why is this method useful for the field of climate adaptation?

The principles of diversification and use of portfolios have high relevance for adaptation. PA allows analysis of these in economic terms. It helps in selecting a set of options that, together, are effective over the range of possible projected future climates, rather than a single option best suited to one possible future, and so has high resonance with iterative risk management (IPCC SREX, 2012).

## Useful resources

Crowe K. A. and Parker, W. H. (2008) Using portfolio theory to guide reforestation and restoration under climate change scenarios. Climatic Change 89: pp.355-370.

Hunt, A. (2009) Economic Aspects of Climate Change Impacts and Adaptation in the UK. PhD Thesis. University of Bath.

Markowitz, H. M. (1952) Portfolio selection. Journal of Finance 7: pp.77-91.

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